I'm looking for a printing firm in the US which can produce a sixty
page folded and stapled booklet with a one colour (+ black and white)
cover in a digest size (about six by eight inches roughly); they must
also be able to envelope or bag the booklets and post them (within the
US and Canada).  The most important thing, though, is that they must
be able to deal with me wholly via email and telephone - I'm in the UK
and I want to produce the same publication simultaneously in the UK
and US, sending copy and address lists to the US printers via email. 
I'd like a list of several printers who meet all these criteria
(between four and twelve, ideally?) who I can ask for quotes.

My best suggestion would be to contact a Kinko's store
(www.kinkos.com), you can actually submit your artwork online through
their website. I'm not particularly sure if they ship internationally,
but it doesn't hurt to ask. We've had them do our brochures from time
to time, i just mail them a CD of our artwork in .PDF format. They'll
even send you proof's before mass-printing so you can check on the
quality of the work and such.

Thanks; that's helpful but not going to work, since I need a firm
which will do the complete service from printing to enveloping,
labelling and mailing.  According to their website, Kinkos could print
but not wrap and mail my stuff for me, and - remember - I'm not in the
USA at all.  I need a firm that can handle the process from receiving
a disc to despatching the finished object for me without needing my
presence except via email/phone.

I could be rude and post this as the answer, but it only took 30
seconds; not worth $30.

http://dmoz.org/Business/Publishing_and_Printing/Printing/Direct_Mail/

205 different direct mail printing companies.  They will accept your
print order, print to spec, send you proofs, and then package and mail
to your mailing list.  Some of them will also generate mailing lists
for you.

I used to work in the direct mail printing industry; we generally
don't care where the client is, as long as the artwork and mailing
list are in good shape.  Camera-read PDF or TIFF files are great. 
Text files for the address list are great.

Enjoy, and good luck!

Search Strategy:

direct mail printing service
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=direct+mail+printing+service